Motion tracking always gives me error messages and acts unpredictably
Everytime you get the "some data failed to reconstruct" error it means only one thing: tracking is not accurate.

Without seeing the video file is hard to determine what is wrong. Post it in some video sharing site and share the link as part of your original question. 

Vague advise is the only thing that is left until you can give more information:

If the video is blurry, shaky or has any kind of motion blur distortion you will have a hard time getting good results when tracking.

Yes, you need at least 8 good trackers,and 8 trackers means 8 solid trackers on a portion of the video where there is useful information. Use the keyframe option so that blender determines what section that is.

Check your trackers one by one on the track window to see if they are slipping or jumping about.

Example of bad tracking:



Accurate tracking:



Make sure that you are using the correct solve model. If the camera is stationary, and the camera is just panning, and tilting, but not being displaced you need to use "tripod" as the solve model, and you will get no 3D information.

There are many tools to help you figure out what is wrong(like the graphs with green, red and blue lines) use them.

Motion Tracking. What do the graphs represent and how are they useful?

There is a very detailed post in this site to help you troubleshoot tracking:

How can I get better results when doing camera motion tracking?

Read it carefuly and follow the links on that post. It makes no sense to repeat all of the info here.